Package 'smoothic'

Boston House Price Data (Original)

Description

Original data, which come from a study by Harrison Jr and Rubinfeld (1978), examining the association between median house prices in a particular community with various community characteristics. See bostonhouseprice2 for the corrected version, with additional variables.

Usage

bostonhouseprice

Format

A data frame with 506 rows and 9 variables:

crime

crimes committed per capita

rooms

average number of rooms per house

radial

index of accessibility to radial highways

stratio

average student-teacher ratio of schools in the community

lowstat

percentage of the population that are "lower status"

lnox

log(annual average nitrogen oxide concentration (pphm))

lproptax

log(property tax per $1000)

ldist

log(weighted distances to five employment centres in the Boston region)

lprice

log(median house price ($))

Source

https://CRAN.R-project.org/package=wooldridge

References

Harrison Jr, D. and Rubinfeld, D. L. (1978). Hedonic housing prices and the demand for clean air. Journal of environmental economics and management, 5(1):81-102.

Wooldridge, J. M. (2015). Introductory econometrics: A modern approach. Cengage learning.

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Boston House Price Data (Corrected Version)

Description

Corrected data, which come from a study by Harrison Jr and Rubinfeld (1978), examining the association between median house prices in a particular community with various community characteristics. See bostonhouseprice for the original version.

Usage

bostonhouseprice2

Format

A data frame with 506 rows and 13 variables:

crim

per capita crime rate by town

zn

proportion of residential land zoned for lots over 25,000 sq.ft

indus

proportion of non-retail business acres per town

rm

average number of rooms per dwelling

age

proportion of owner-occupied units built prior to 1940

rad

index of accessibility to radial highways

ptratio

pupil-teacher ratio by town

lnox

log(nitric oxides concentration (parts per 10 million))

ldis

log(weighted distances to five Boston employment centres)

ltax

log(full-value property-tax rate per USD 10,000)

llstat

log(percentage of lower status of the population)

chast

Charles River dummy variable (=1 if tract bounds river; 0 otherwise)

lcmedv

log(corrected median value of owner-occupied homes in USD 1000's)

Source

https://CRAN.R-project.org/package=mlbench

References

Harrison Jr, D. and Rubinfeld, D. L. (1978). Hedonic housing prices and the demand for clean air. Journal of environmental economics and management, 5(1):81-102.

Leisch F, Dimitriadou E (2021). mlbench: Machine Learning Benchmark Problems. R package version 2.1-3.

---

City Crime Data

Description

Data relating to crime rates per one million residents in 50 U.S cities, taken from Thomas (1990).

Usage

citycrime

Format

A data frame with 50 rows and 7 variables:

violent

reported violent crime rate per 100,000 residents

funding

annual police funding per resident ($)

hs

percentage of people 25 years+ with 4 years of high school

not_hs

percentage of 16 to 19 year-olds not in high school and not high school graduates

college

percentage of 18 to 24 year-olds in college

college4

percentage of people 25 years+ with at least 4 years of college

crime_rate

total overall reported crime rate per 1 million residents

Source

https://hastie.su.domains/StatLearnSparsity_files/DATA/crime.txt

References

Thomas, G.S., 1990. The Rating Guide to Life in America's Small Cities. Prometheus Books, 59 John Glenn Drive, Amherst, NY 14228-2197.

Hastie, T., Tibshirani, R. and Wainwright, M., 2015. Statistical learning with sparsity: the lasso and generalizations. CRC press.

---

Diabetes Data

Description

Data relating to a study of disease progression one year after baseline.

Usage

diabetes

Format

A data frame with 442 rows and 11 variables:

AGE

age of the patient

SEX

sex of the patient

BMI

body mass index of the patient

BP

blood pressure of the patient

S1

blood serum measurement 1

S2

blood serum measurement 2

S3

blood serum measurement 3

S4

blood serum measurement 4

S5

blood serum measurement 5

S6

blood serum measurement 6

Y

quantitative measure of disease progression one year after baseline

Source

https://CRAN.R-project.org/package=lars

References

Efron, B., Hastie, T., Johnstone, I., Tibshirani, R., et al. (2004). Least angle regression. The Annals of Statistics.

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Prostate Cancer Data

Description

Data, which come from a study by Stamey et al. (1989), examining the correlation between the level of prostate-specific antigen (PSA) and various clinical measures in men who were about to receive a radical prostatectomy.

Usage

pcancer

Format

A data frame with 97 rows and 9 variables:

lcavol

log(cancer volume (cm^3))

lweight

log(prostate weight (g))

age

age of the patient

lbph

log(amount of benign prostatic hyperplasia (cm^2))

svi

presence of seminal vesicle invasion (1=yes, 0=no)

lcp

log(capsular penetration (cm))

gleason

Gleason score

pgg45

percentage of Gleason scores four of five

lpsa

log(PSA (ng/mL))

Source

https://web.stanford.edu/~hastie/ElemStatLearn/datasets/prostate.data

References

Stamey, T. A., Kabalin, J. N., McNeal, J. E., Johnstone, I. M., Freiha, F., Redwine, E. A., and Yang, N. (1989). Prostate specific antigen in the diagnosis and treatment of adenocarcinoma of the prostate. ii. radical prostatectomy treated patients. The Journal of urology, 141(5):1076-1083.

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Plot conditional density curves

Description

This function plots the model-based conditional density curves for different effect combinations. For example, take a particular covariate that is selected in the final model. The other selected covariates are fixed at their median values by default (see covariate_fix to fix at other values) and then the plotted red and blue densities correspond to the modification of the chosen covariate as “low” (25th quantile by default) and “high” (75th quantile by default).

Usage

plot_effects(
  obj,
  what = "all",
  show_average_indiv = TRUE,
  p = c(0.25, 0.75),
  covariate_fix,
  density_range
)

Arguments

obj	An object of class “smoothic” which is the result of a call to smoothic.
what	The covariate effects to be plotted, default is what = "all". The user may supply a vector of covariate names to be plotted (only covariates selected in the final model can be plotted).
show_average_indiv	Should a “baseline” or “average” individual be shown, default is show_average_indiv = TRUE. If show_average_indiv = FALSE then this is not shown.
p	The probabilities given to the quantile function. This corresponds to the plotted red and blue density curves where the chosen covariate is modified as “low” and “high”. The default is p = c(0.25, 0.75) to show the 25th and 75th quantiles.
covariate_fix	Optional values to fix the covariates at that are chosen in the final model. When not supplied, the covariates are fixed at their median values. See the example for more detail.
density_range	Optional range for which the density curves should be plotted.

Value

A plot of the conditional density curves.

Author(s)

Meadhbh O'Neill

Examples

# Sniffer Data --------------------
# MPR Model ----
results <- smoothic(
  formula = y ~ .,
  data = sniffer,
  family = "normal",
  model = "mpr"
)
plot_effects(results)

# Only plot gastemp and gaspres
# Do not show the average individual plot
# Plot the lower and upper density curves using 10th quantile (lower) and 90th quantile (upper)
# Fix violent to its violent to 820 and funding to 40

plot_effects(results,
             what = c("gastemp", "gaspres"),
             show_average_indiv = FALSE,
             p = c(0.1, 0.9),
             covariate_fix = c("gastemp" = 70,
                               "gaspres" = 4))

# The curves for the gastemp variable are computed by fixing gaspres = 4 (as is specified
# in the input). The remaining variables that are not specified in covariate_fix are fixed
# to their median values (i.e., tanktemp is fixed at its median). gastemp is then modified
# to be low (10th quantile) and high (90th quantile), as specified by p in the function.

---

Plot the $\epsilon$-telescope coefficient paths

Description

This function plots the standardized coefficient values with respect to the $\epsilon$-telescope for the location (and dispersion) components.

Usage

plot_paths(
  obj,
  log_scale_x = TRUE,
  log_scale_x_pretty = TRUE,
  facet_scales = "fixed"
)

Arguments

obj	An object of class “smoothic” which is the result of a call to smoothic.
log_scale_x	Default is log_scale_x = TRUE, which uses a log scale on the x-axis. If log_scale_x = FALSE, then the raw values of the $\epsilon$-telescope are plotted.
log_scale_x_pretty	Default is log_scale_x_pretty = TRUE, where the x-axis labels are “pretty”. epsilon_1 and epsilon_T must be a number to the power of 10 for this to apply.
facet_scales	Default is facet_scales = "fixed". This is supplied to facet_wrap.

Value

A plot of the standardized coefficient values through the $\epsilon$-telescope.

Author(s)

Meadhbh O'Neill

Examples

# Sniffer Data --------------------
# MPR Model ----
results <- smoothic(
  formula = y ~ .,
  data = sniffer,
  family = "normal",
  model = "mpr"
)
plot_paths(results)

---

Predict smoothic

Description

predict method class “smoothic”

Usage

## S3 method for class 'smoothic'
predict(object, newdata, ...)

Arguments

object	an object of class “smoothic” which is the result of a call to smoothic.
newdata	new data object
...	further arguments passed to or from other methods.

Value

a matrix containing the predicted values for the location mu and scale s

Author(s)

Meadhbh O'Neill

Examples

# Sniffer Data --------------------
# MPR Model ----
results <- smoothic(
  formula = y ~ .,
  data = sniffer,
  family = "normal",
  model = "mpr"
)
predict(results)

---

Variable Selection Using a Smooth Information Criterion (SIC)

Description

Implements the SIC $\epsilon$-telescope method, either using single or multiparameter regression. Returns estimated coefficients, estimated standard errors and the value of the penalized likelihood function. Note that the function will scale the predictors to have unit variance, however, the final estimates are converted back to their original scale.

Usage

smoothic(
  formula,
  data,
  family = "sgnd",
  model = "mpr",
  lambda = "log(n)",
  epsilon_1 = 10,
  epsilon_T = 1e-04,
  steps_T = 100,
  zero_tol = 1e-05,
  max_it = 10000,
  kappa,
  tau,
  max_it_vec,
  stepmax_nlm
)

Arguments

formula	An object of class "formula": a two-sided object with response on the left hand side and the model variables on the right hand side.
data	A data frame containing the variables in the model; the data frame should be unstandardized.
family	The family of the model, default is family = "sgnd" for the "Smooth Generalized Normal Distribution" where the shape parameter kappa is also estimated. Classical regression with normally distributed errors is performed when family = "normal". If family = "laplace", this corresponds to a robust regression with errors from a Laplace-like distribution. If family = "laplace", then the default value of tau = 0.15, which is used to approximate the absolute value in the Laplace density function.
model	The type of regression to be implemented, either model = "mpr" for multiparameter regression (i.e., location and scale), or model = "spr" for single parameter regression (i.e., location only). Defaults to model="mpr".
lambda	Value of penalty tuning parameter. Suggested values are "log(n)" and "2" for the BIC and AIC respectively. Defaults to lambda ="log(n)" for the BIC case. This is evaluated as an R expression, so it may be a number of some function of n.
epsilon_1	Starting value for $\epsilon$-telescope. Defaults to 10.
epsilon_T	Final value for $\epsilon$-telescope. Defaults to 1e-04.
steps_T	Number of steps in $\epsilon$-telescope. Defaults to 100, must be greater than or equal to 10.
zero_tol	Coefficients below this value are treated as being zero. Defaults to 1e-05.
max_it	Maximum number of iterations to be performed before the optimization is terminated. Defaults to 1e+04.
kappa	Optional user-supplied positive kappa value (> 0.2 to avoid computational issues) if family = "sgnd". If supplied, the shape parameter kappa will be fixed to this value in the optimization. If not supplied, kappa is estimated from the data.
tau	Optional user-supplied positive smoothing parameter value in the "Smooth Generalized Normal Distribution" if family = "sgnd" or family = "laplace". If not supplied then tau = 0.15. If family = "normal" then tau = 0 is used. Smaller values of tau bring the approximation closer to the absolute value function, but this can cause the optimization to become unstable. Some issues with standard error calculation with smaller values of tau when using the Laplace distribution in the robust regression setting.
max_it_vec	Optional vector of length steps_T that contains the maximum number of iterations to be performed in each $\epsilon$-telescope step. If not supplied, max_it is the maximum number of iterations performed for 10 steps and then the maximum number of iterations to be performed reduces to 10 for the remainder of the telescope.
stepmax_nlm	Optional maximum allowable scaled step length (positive scalar) to be passed to nlm. If not supplied, default values in nlm are used.

Value

A list with estimates and estimated standard errors.

• coefficients - vector of coefficients.

• see - vector of estimated standard errors.

• model - the matched type of model which is called.

• plike - value of the penalized likelihood function.

• kappa - value of the estimated/fixed shape parameter kappa if family = "sgnd".

Author(s)

Meadhbh O'Neill

References

O'Neill, M. and Burke, K. (2023) Variable selection using a smooth information criterion for distributional regression models. <doi:10.1007/s11222-023-10204-8>

O'Neill, M. and Burke, K. (2022) Robust Distributional Regression with Automatic Variable Selection. <arXiv:2212.07317>

Examples

# Sniffer Data --------------------
# MPR Model ----
results <- smoothic(
  formula = y ~ .,
  data = sniffer,
  family = "normal",
  model = "mpr"
)
summary(results)

---

Sniffer Data

Description

Data examining the factors that impact the amount of hydrocarbon vapour released when gasoline is pumped into a tank.

Usage

sniffer

Format

A data frame with 125 rows and 5 variables:

tanktemp

initial tank temperature (degrees F)

gastemp

temperature of the dispensed gasoline (degrees F)

tankpres

initial vapour pressure in the tank (psi)

gaspres

vapour pressure of the dispensed gasoline (psi)

y

hydrocarbons emitted (g)

Source

https://CRAN.R-project.org/package=alr4

References

Bedrick, E.J. (2000). Checking for lack of fit in linear models with parametric variance functions. Technometrics 42 (3), 226–236.

Weisberg, S. (2014). Applied Linear Regression, 4th edition. Hoboken NJ: Wiley.

---

Summarising Smooth Information Criterion (SIC) Fits

Description

summary method class “smoothic”

Usage

## S3 method for class 'smoothic'
summary(object, ...)

Arguments

object	an object of class “smoothic” which is the result of a call to smoothic.
...	further arguments passed to or from other methods.

Value

A list containing the following components:

• model - the matched model from the smoothic object.

• coefmat - a typical coefficient matrix whose columns are the estimated regression coefficients, estimated standard errors (SEE) and p-values.

• plike - value of the penalized likelihood function.

Author(s)

Meadhbh O'Neill

Examples

# Sniffer Data --------------------
# MPR Model ----
results <- smoothic(
  formula = y ~ .,
  data = sniffer,
  family = "normal",
  model = "mpr"
)
summary(results)

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